Stream 4: Diamond Light Source Session 1

The formation of nanoporous structures by selective removal of an active component of an alloy is an important process for both the development of novel functional nanomaterials, and for understanding the degradation behaviour of complex alloy systems. The structures that form are complex, 3-dimensionally interconnected porous networks that undergo self-similar coarsening to form highly reactive ‘sponge-like’ materials. The electrochemical nature of the process means that operando approaches are needed to follow the dynamics of formation, but the extremely small size of the pores means that high resolution imaging is required to fully elucidate the structures. In this talk we will discuss correlative approaches using both electron and X-ray techniques to study two examples of the dealloying phenomena: i) the reactivity of CoCr wear particle debris from metal hip implants and ii) the formation of nanoporous noble metals (Au, Pt). Dynamic imaging of the dealloying process, and well as operando studies of pore formation, and the accompanied strain dynamics in the system, will be presented.

This work aims to develop a workflow that combines both informed and data-driven approaches to condensing the dimensionality of the electron diffraction data. Using these ‘latent space’ representations of the scanned region, we can apply clustering algorithms to identify regions of similar character. By combining the results of multiple autonomous approaches, we would be able to map domains within the crystal and associate a level of confidence to given classifications. Incorporating this as a pre-processing unsupervised workflow would drastically improve the ability to characterise the nano-scale structure of materials, both through the production of significantly signal-boosted diffraction data and reduction in the laborious manual investigation.

With the advent of fast direct-electron detectors, capturing large scan arrays of electron diffraction data is becoming more and more accessible. The scanning electron nanobeam diffraction technique lends itself well to microscope automation and can cover areas in the micrometres length scale and hence, while still capturing microstructural details not accessible via powder x-ray diffraction (PXRD), provides statistically significant insight into the crystallographic defects and domain morphology in the microstructure. Larger probe sizes and lower magnifications typically used in SEND also result in reduced electron dose on the sample, compared to atomic-resolution STEM, making this technique suitable for beam-sensitive phases. The quantity of SEND data collected during a day on the microscope can run well above 1TB. This is far more information than can be comprehensively processed by hand within a reasonable time frame. As a case study, we are implementing this approach to study the complex microstructure that drives leading Sodium-ion battery materials.

The sodium-ion batteries we investigated are among the best worldwide with performances that are comparable with Li-ion batteries using LiFePO₄ as cathode material. Our cathode materials are based on the same layered metal oxide structures as the commercial lithium NMC and NCA cathodes but have a more complex structural polymorphism. These structures have been variously labelled P3, O2, OP4, Z, Z’, O3’, O3’’ and O3’’’, however, these labelled phases rarely exist in any extended form as the intercalation process is largely stochastic. Comprehensive knowledge of the different structures is essential for our understanding of these materials and, due to the potential complexity of phase disposition, these materials lend themselves to our unsupervised domain mapping approach. 

We have investigated a number of state-of-the-art unsupervised learning approaches to reduce the dimensionality of our datasets and to represent them on a lower-dimension manifold. For the SEND data collection, we aligned a JEOL Grand-ARM microscope at 300 kV with the probe corrector optics turned off, allowing us to reduce the probe convergence semi-angle to around 1 mrad. We collected the diffraction data on a MerlinEM quad detector (Quantum Detectors) with each dataset reshaping to 256x256 in the probe scanning plane and 515x515 on the diffraction plane. 

As an example, we present the results of this workflow, using a combination of Common Peak Selection (for initial dimensionality reduction with minimal information loss)– t-distributed Stochastic Neighbour Embedding (for further non-linear dimensionality reduction and cluster separation) and Gaussian Mixture Model (for clustering the data). This approach produced a domain map with plausible phase dispositions as seen in Figure 1. 

Figure 1 – (a) the original unmapped scan region, (b) the two-dimensional representation of the key peak data reduced using a t-distributed Stochastic Neighbour Embedding (t-SNE) and clustered with a Gaussian Mixture Model (GMM) (note that the cluster at [0,0] corresponds to the uncomputed background regions was added afterwards for completeness), (c) a domain map produced from the clusters present in the manifold, (d) the composite diffraction patterns pertaining to the identified regions

The incoherence of some of the composite diffraction data along with the busier regions in the map, highlight the utility that will be provided by comparing multiple complementary domain maps to improve the confidence of the classification. A multi-prong approach is advantageous as any individual low dimensionality representation will result in a loss of information (the extent of this depends on the ‘inherent’ dimensionality of the data) and so using multiple representations allows us to combine different domain maps with different intrinsic information retained in order to segment the data in a way that still reflects all the information initially available.

Unsupervised Machine Learning, Domain Mapping, Cluster Analysis, Structure Analysis, Structure Determination, Energy Materials, SEND Data Processing

Long before the advent of iterative methods for the solution of the ptychographical phase-retrieval problem for lensless, high-fidelity transmission microscopy [1], a direct deconvolution method was well-developed in the 1990s, called Wigner Distribution Deconvolution [2]. This included work showing that the ptychographic data set could be inverted ‘blindly’, i.e. without any knowledge of the illumination optics [3]. However, there were problems with the method reported. The technique used a process called ‘stepping out’ that could only employ a tiny fraction of the massive data set involved in WDD. Since then, Li et al [4] have developed a much more comprehensive way of dealing with all pairs of phase differences in a typical WDD data set. The present work revisits the blind deconvolution problem in the light of this more recent work. Whether WDD will compete with the iterative solution methods, all of which solve for both the object function and the illumination field, and which are very well developed and flexible in their application, is yet to be determined. Whatever the case, handling the blind deconvolution issue robustly is a key requirement for handling this sort of ‘4D STEM’ data. We present recent progress in achieving this goal.

Phase retrieval, Ptychography, Wigner Distribution Deconvolution 

1. Rodenburg, J. and A. Maiden, Ptychography, in Springer Handbook of Microscopy, P.W. Hawkes and J.C.H. Spence, Editors. 2019, Springer International Publishing: Cham. p. 2-2.

2. Rodenburg, J. and R. Bates, The theory of super-resolution electron microscopy via Wigner-distribution deconvolution. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 1992. 339(1655): p. 521-553.

3.  McCallum, B. and J. Rodenburg, Simultaneous reconstruction of object and aperture functions from multiple far-field intensity measurements. JOSA A, 1993. 10(2): p. 231-239.

4. Li, P., T.B. Edo and J.M. Rodenburg, Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design. Ultramicroscopy, 2014. 147: p. 106-113.

Molecular materials like metal–organic frameworks (MOFs), hybrid, and organic materials exhibit critical electron doses as low as <10 e^-Å^-2 setting substantial challenges for controlling and monitoring beam-sample interactions for access to information on the native state of molecular solids. This presentation will discuss advances for diffraction and imaging for insights into structural organisation in these materials on the 1-1000 nm length scale. 

MOFs, comprised of metal cations or metal clusters connected by organic linker molecules in an extended network, exhibit properties of substantial interest for applications in gas storage, separations, and catalysis. Hierarchical organisation possible in MOF crystals and glasses has prompted efforts to interrogate interfaces and grain structure in MOFs. Low-dose scanning electron diffraction (SED) with direct electron detection has enabled access to structural information on these scales for the identification of crystalline domains in MOF crystal-glass composites and virtual dark field imaging of correlated defect nano-domains in UiO-66 [1]. Coupled with lattice-resolution imaging in STEM, these analyses provide insight into faceting, domain orientation and size, and surface termination in UiO-66 crystals. This presentation will highlight further examples of imaging and diffraction from MOF materials for distinguishing crystallographic phases. Applications of SED to determine crystalline structures in organic and hybrid materials will also be discussed.

Scanning electron diffraction, scanning transmission electron microscopy, metal–organic frameworks, hybrid materials